[Junior]

How does natural selection reduce the time required for random mutations to occur and to be incorporated into the genome?

Individuals without the mutation will be less likely to procreate. Those with the gene will then pass it on to a higher percentage of offspring than those without. Eventually, the mutation spreads throughout the population.

[bluejay]

Individuals without the mutation will be less likely to procreate. Those with the gene will then pass it on to a higher percentage of offspring than those without. Eventually, the mutation spreads throughout the population.

All that means is that failed mutations do not succeed. This does not make it more likely that a beneficial mutation occurs in the first place.